Select the formula for the Volume of the cone 2. T:r·h+ 2·T• r2 1 T• p2 . h 3 O2. T. r2 . h T:r·h² + T · r2

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

A: Given: To find the volume V generated by rotating the given region about the line AB

Q: Find the volume of the solid that lies under the sphere: x2 +y? +z? -2z=0 and above the cone: z=3(x²…

A: Solid lies under the sphere x2+y2+z2-2z=0⇒x2+y2+z-12=1 and above the cone z=3x2+y2 Now z=3x2+y2 and…

Q: Find the volume of the part of the ball p < 1 that lies between the cones o = 1/4 and ø = r/3. -1+ 2…

A: We have to find the volume of the part of the ball rho&lt;=1 that lies between the cones phi = π/4…

Q: Find the volume of the solid cut from the cylinder x? + y? = 100 by the planes z = O and a + z = 7.

A:

Q: ® Eualuate the inteyral- ... taken. throughout the volume o f sphere b=2+

A: To evaluate ∫∫∫1a2-x2-y2-z2dx dy dz Taken throughout the volume of sphere x2+y2+z2=a2

Q: 25. Find the volume of the solid that is enclosed by the cone z = Vx² + y? and the sphere 22 + y? +…

A:

Q: 2. Find the volume of the wedge cut from the cylinder r? + y? = 1 by the planes z = -y and z = 0.

A: Given the wedge cut from the cylinder x2+y2=1 by the planes z=-y and z=0.

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

A: Given: a=3, b=3

Q: What is the volume of the region which lies between the spheres p 3 and p 2 cos o, and inside the…

A:

Q: (a) Find the volume V of the wedge shown in the figure. Top: y + z = 1 Side:

A: In this question we will use basic of calculus i.e application of integration. We will use concept…

Q: Find the volume of the pyramid with base in the plane z = -11 and sides formed by the three planes y…

A:

Q: Find the volume of the part of the ball p < a that lies between the cones o = T/6 and ¢ = T/3. = 10

A: Given ball ρ≤a lies between cones ϕ=π6 and ϕ=π3.

Q: Find the volume of the cone. 9 m 5 m What is the volume V in terms of 1? v=m3 V = (Type an exact…

A: We are given with the cone whose radius is 5 m  height is 9 cm and need to find the volume.

Q: b) Find the volume of an inverted cone defined by: i. R< 2 and 0 <0 <"/3

A: the given question is taken from the calculus in which we have to find the volume of the cone so…

Q: R) If V=i +2j+3K, V,szi +2j+2K, V = 3(+3 j +K, find the Volume?

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Q: Find the real number b such that the volume of solid B (r, +

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Q: Find the volume of the region enclosed by the cylinder x2 + y? = 2, the plane z – x+ y= 0 and the…

A: We have,

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: We need to evaluate volume.

Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. The volume…

A: Given, a=0 b=10 3x+5y=30 y= (30-3x)/5= f(x)

Q: Q3-Find the volume common by the plane x+y=a? & x*+z=a? ?

A:

Q: Find the volume of the cone. 9 m 5m What is the volume V in terms of x? V-m3 (Type an exact answer…

A: We can find the volume as below.

Q: Find the volume of the solid cut from the cylinder x2 + y? = 25 by the planes z = 0 and x + z = 2.

A:

Q: Find the volume of S above the cone where z V + y and inside the sphere where a+ y? + 2 <9.

A: Let S be the region above the cone z=x2+y2 and inside the sphere x2+y2+z2≤9.

Q: Find the volume of the solid lying above the cone z = /x² + y2 and below the sphere x² + y + z? = 8.…

A: In spherical coordinates,                             The volume of a solid is,…

Q: nd the volume of the frustum of a cone of its height h, e lower base radius R, and the upper base…

A:

Q: Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by the…

A:

Q: Find the volume of the solid lying above the cone z = Vr2 + y? and below the sphere a? + y? + z? =…

A:

Q: Find the volume of the solid lying above the cone z = +y? and below the sphere z + y² + z? = 4.

A: Cone:-  z2 = x2+y2 Sphere:- x2+y2+z2 = 4

Q: The volume of the solid given by the two surfaces is z = 8 - 3(x? + y*), z = (x? + y")2 - 2

A:

Q: Which of the following is the volume of the solid lying above the square defined by 0 < * < 1 and 1<…

A:

Q: What is the volume of the region which lies between the spheres p = 3 and p= 2 cos o, and inside the…

A: Volume is a 3-dimensional quantity which describes the amount of space available in solid. Volume of…

Q: 2. Sketch the given solid. Find its volume. The solid lies inside a?+y?+22 = 2 and outside x² = 2²…

A:

Q: Q3: Find the volume of the solid that lies above the cone x2 = z2 + y? x = 8 – (z? + y²). and under…

A:

Q: e want to compute the volume of the tetrahedron cut from the fir ane 6x + 3y + 2z = 6. Which one is…

A:

Q: Find the volume inside the sphere (r = a) that lies between the cones ($ = n/3) and ($ = 2n/3) %3D…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: ind the volume of the solid lying above the cone z = Vx² + y2 and below the sphere =2 + y? + z² = 1.…

A:

Q: Find the volume of the cone. Enter the answer in terms of z. 31 in. 24 in. The volume of the cone is…

A: Explanation and solutions is given below.....

Q: Find the volume of the cone. Either enter an exact answer in terms of T or use 3.14 for T. 5 units3

A:

Q: Which of the following is the volume of the solid lying above the square defined by 0 <x <1 and1< y<…

A:

Q: Find the volume of the region enclosed by the cone z = x² + y² and the sphere r2 + y? + z² = 4.

A: Solve for volume

Q: Find the volume of the cylinder in terms of x. The diagrams are not drat 15 m 10. 1.7 m .3

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Q: 29. Find the volume of the part of the ball p < a that lies between the cones o = r/6 and ø = T/3.

A: Here,  Φ lies between π6 and π3. θ lies between 0 and 2π. ρ lies between 0 to a.

Q: Find the volume of the solid cut from the cylinder a? + y? = 100 by the planes z = 0 and a + z = 7.…

A:

Q: (c) Find the volume of the solid region above the cone z? = 3(x² + y²) (z20) and below the sphere x?…

A:

Q: 1. Find the volume of the sphere. Leave your answer in terms of T. r = 4

A: Finding the volume of sphere when radius is given

Q: A) Find the volume of the solid that is bounded below by the hemispherep = 1, z>0 and above by the…

A:

Q: Find the volume.

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Q: Determine the solution in finding the dimensions of the right circular cylinder, with the greatest…

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Q: Find the real number b such that the volume of solid B = (r, y, z) | a² + y² + z2 < Pand 0 2 5 be…

A:

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=3 is O a. 4 3 O…

A: If we have a plane of the form x/a + y/b + z/c = 1 then x intercept at (a,0,0) , y intercept at…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.